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Hyperparametric Robust and Dynamic Influence Maximization

Arkaprava Saha, Bogdan Cautis, Xiaokui Xiao, Laks V. S. Lakshmanan

TL;DR

This work addresses robust influence maximization on dynamic diffusion networks where edge probabilities are given by a hyperparametric function p_e = H(\theta, x_e). It introduces RIME, a method that combines multiplicative weight updates over a sampled hyperparameter set with a greedy RR-set based seed finder to maintain high-quality seeds as the network evolves, including node/edge insertions and deletions. The authors prove bi-criteria approximation guarantees with high probability and derive an amortized running time bound that scales with the number of hyperparameters and dynamic factors. Empirically, RIME achieves orders-of-magnitude speedups over restarting IM from scratch while delivering seed sets with competitive or superior worst-case influence across the hyperparameter space on both synthetic and real networks.

Abstract

We study the problem of robust influence maximization in dynamic diffusion networks. In line with recent works, we consider the scenario where the network can undergo insertion and removal of nodes and edges, in discrete time steps, and the influence weights are determined by the features of the corresponding nodes and a global hyperparameter. Given this, our goal is to find, at every time step, the seed set maximizing the worst-case influence spread across all possible values of the hyperparameter. We propose an approximate solution using multiplicative weight updates and a greedy algorithm, with provable quality guarantees. Our experiments validate the effectiveness and efficiency of the proposed methods.

Hyperparametric Robust and Dynamic Influence Maximization

TL;DR

This work addresses robust influence maximization on dynamic diffusion networks where edge probabilities are given by a hyperparametric function p_e = H(\theta, x_e). It introduces RIME, a method that combines multiplicative weight updates over a sampled hyperparameter set with a greedy RR-set based seed finder to maintain high-quality seeds as the network evolves, including node/edge insertions and deletions. The authors prove bi-criteria approximation guarantees with high probability and derive an amortized running time bound that scales with the number of hyperparameters and dynamic factors. Empirically, RIME achieves orders-of-magnitude speedups over restarting IM from scratch while delivering seed sets with competitive or superior worst-case influence across the hyperparameter space on both synthetic and real networks.

Abstract

We study the problem of robust influence maximization in dynamic diffusion networks. In line with recent works, we consider the scenario where the network can undergo insertion and removal of nodes and edges, in discrete time steps, and the influence weights are determined by the features of the corresponding nodes and a global hyperparameter. Given this, our goal is to find, at every time step, the seed set maximizing the worst-case influence spread across all possible values of the hyperparameter. We propose an approximate solution using multiplicative weight updates and a greedy algorithm, with provable quality guarantees. Our experiments validate the effectiveness and efficiency of the proposed methods.

Paper Structure

This paper contains 15 sections, 5 theorems, 29 equations, 5 figures, 8 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Diffusion Models and Influence Functions
  5. Robust Influence Maximization
  6. Dynamic Diffusion Networks
  7. Problem Statement and Hardness
  8. Solution
  9. Algorithm
  10. Analysis
  11. Experiments
  12. Experimental Setup
  13. Results
  14. Parameter Sensitivity Analysis
  15. Conclusion

Key Result

Lemma 1

Our greedy algorithm returns a seed set $\hat{S}$ such that $F\left(\hat{S}\right) \geq (1 - 1/e - \gamma - \epsilon_1) \cdot OPT$, where

Figures (5)

  • Figure 1: Running time comparison on synthetic / real-world networks for incremental (top row) / fully dynamic (bottom row) settings.
  • Figure 2: Solution quality comparison on synthetic / real-world networks for incremental (left) and fully dynamic (right) settings.
  • Figure 3: Running time and solution quality comparison on more networks in the incremental setting.
  • Figure 4: Variation of running time and solution quality with $k$ on the Weibo network in the incremental setting.
  • Figure 5: Variation of solution quality with $l$ and $T$ for different values of $B$ on the Weibo network in the incremental setting.

Theorems & Definitions (8)

  • Lemma 1
  • proof
  • Lemma 2
  • Corollary 1
  • Lemma 3
  • proof
  • Theorem 1
  • proof